UK DM project:
radioactivity test results

Useful numbers and relationships

A concentration C (g/g) of an element with activity1Bg Bq g-1
in a 4p shield results in a g flux
at the centre of that shield of:

F (cm-2
s-1) = CBglg(1 - e-x/lg);

(1)

reducing to:

F»CBgx

(1a)

for thin shields, where x is shield thickness in g cm-2
( i.e. the activity is reduced by a factor x/lg compared with a thick slab). The attenuation
length lg is of
order 20-25 g cm-2 for a typical equilibrium photon
cascade.

Some data are presented as total a-counts (usually in counts
per hour per cm2); though these cannot be unambiguously
related to source activities (because a ranges are
energy-dependent and very short), they can be used to place approximate upper limits on U
or Th concentration or on 210Pb activity. Numerical
integration over a spectra and approximate ranges result in:

For an isotope of mass Ai AMU and half-life t½ years, the number of atoms required to give one disintegration
per day is:

Ni = 527 t½;

(2)

and the mass concentration to give one disintegration per day per kg is:

C = 8.75 ´ 10-25Ait½.

(3)

If the isotope is present in the natural element (mean atomic mass A) with an
atomic fraction fi, then these become:

N = 527 t½fi

(2a)

C = 8.75 ´ 10-25Ait½/fi;

(3a)

for a chain of n decays (from Th or U), these must be divided by n.
For Th, n = 10; for U, there is the added complication that 95.6% of primary
decays are 238U (n = 14), and 4.4% 235U (n = 11), giving n = 13.87.

For materials external to the target, the short-range a, b particles have low probability of producing `events' - though
bremsstrahlung from higher energy bs must be considered.
Consequently, we are generally only concerned with the g
activity, for which we have (X-rays not included):-

ng = 0.107(K),
2.65(Th), 2.20(U).

In the target itself, b activity is also relevant (a decays, being contained within the target apart from those within a
few mm of the target surface, should be rejected by their ~ MeV
energies), and we have:-

nb = 0.893(K),
4(Th), 5.91(U).

Hence:

1 ppm K

®

0.0309 Bq kg-1

=

1.86 dpm kg-1

=

2.67 ktru;

®

0.00331 Bq kg-1

=

0.199 dpm kg-1

=

0.286 ktru in g

(ppm = parts per million);

alternatively,

1 Bq kg-1 of 40 K ®
32.3 ppm K; 1 Bq kg-1 in g® 302 ppm K.

For disintegrations of the parent232Th
(or any daughter on a 100% branch), we have:

Strictly, the becquerel (Bq) and other disintegration units refer to the
totality of decays and not, as here, to the decays in a particular branch. However, this
(ab)usage is very convenient, and careful use should cause no ambiguity.

The introduction of a `total rate unit' (tru) arises from the decision
to adopt a standard `differential rate unit' (dru) of 1 event per keV per day per kg for
background spectra. Integration then gives 1 tru = 1 per day per kg (1 Mtru = 106 per day per kg).